In recent years the thermo-acoustical study of molecular interactions in various binary liquid mixtures has got considerable importance in developing theoretical models as well as its application in industry and engineering [1-4]. The study of intermolecular interaction is of considerable importance for the elucidation of formation of complexes and plays an important role in the study liquid mixtures. The properties which may be regarded as useful for the interpretation of molecular interaction and molecular association in binary mixtures are mainly density, refractive index, ultrasonic velocity, sound velocity, compressibility, molar volume, free volume, intermolecular free length, Rao's constant etc.

The aim of present study is to investigate the variation of thermo acoustical parameters of binary liquid mixture of aqueous solutions of Lithium sulphate and Lithium chloride with variable molar concentrations and temperatures. The variation of these parameters with molar concentration may be helpful in pharmaceutical and food industries to prepare various drug dosages, solution, tablets, capsule, gel and injection in solution form [5-9].

The chemicals Lithium Chloride (LiCl) and Lithium sulphate (Li₂SO₄) used in the present work were the products of AR grade with minimum assay of 99.9%. Therefore, all these chemicals were used without further purification. 

The solutions were left for sufficient time to allow them to have complete ionization. The binary mixtures of desired compositions were prepared by mixing known volumes of two prepared solutions. The ultrasonic velocities were measured at 2MHz with a single crystal variable path interferometer (F-81 D Mittal make) with an accuracy of 0.01%. The densities of aqueous solutions and mixtures were measured with a pycnometer of bulb volume 10cc. The viscosity of the liquids was measured by an Ostwald Viscometer.

The thermo-acoustical parameters such as Intermolecular free Length (L_f), relaxation Time (t), Molar Volume (V_m) and Molar sound Velocity (R) have been calculated using standard empirical relations [10-14].

The experimental values of viscosity and calculated values of Intermolecular free length (L_f), relaxation time (t), Molar volume (V_m) and Molar sound velocity (R) with the varying mole fractions of the binary mixture and with the varying temperature are presented in Tables 1-5 using experimental values of density and ultrasonic velocity reported somewhere else [15]. The variations of these parameters with varying mole fraction are also presented in Figure 1-5 for the binary mixtures.

Viscosity

Figure 1 shows that the viscosity of binary mixture increases non linearly with increasing mole fraction of Li₂ SO₄. The increase in viscosity of the solution on increasing salt concentration is confirmed by some other workers [13,17]. At a specific mole fraction (0.7) of Li₂SO₄ the viscosity shows a sudden decrease in its value. On further increasing the mole fraction of Li₂SO₄ the viscosity again starts rising which confirms the solute-solvent interactions in the mixture. The sudden decrease in viscosity occurs at the specific mole fraction 0.7which is same as obtained for the ultrasonic velocity, which supports the formation of complexes at 0.7 mole fraction of Li₂SO₄ in binary mixture. As usual on increasing the temperature the viscosity of mixture decreases for all mole fractions and the amount by which the viscosity suddenly decreases at complex forming mole fraction (0.7) is more at higher temperature.

Table 1: Values of Viscosity (Centipoise) for the Binary Mixture of LiCl and Li₂SO₄ with Varying Mole Fraction 

Table 2: Values of Inter Molecular Free Length (L_f°) for the Binary Mixture of LiCl and Li₂SO₄ with Varying Mole Fraction 

Table 3: Values of Relaxation Time (×10^-10 sec.) for the Binary Mixture of LiCl and Li₂SO₄ with Varying Mole Fraction 

Table 4: Values of Molar Volume (m³/mole) for the Binary Mixture of LiCl and Li₂SO₄ with Varying Mole Fraction 

Table 5: Values of Molar Sound Velocity for the Binary Mixture of LiCl and Li₂SO₄ with Varying Mole Fraction 

Figure 1: Variation of Viscosity (Centipoise) for the Binary Mixture of LiCl and Li₂SO₄ with Varying Mole Fraction

Figure 2: Variation of Inter Molecular Free Length (A°) for the Binary Mixture of LiCl and Li₂SO₄ with Varying Mole Fraction

Intermolecular Free Length (L_f)

The values of intermolecular free length (L_f) for binary mixture at temperature 303K, 308K, 313K and 318K are presented in Table 2. Intermolecular free length in binary liquid mixtures can be used to access the attraction between the component molecules. It denotes the magnitude of either the ion-ion interaction or the ion solvent interaction or both in a binary mixture. Intermolecular free length depends upon the adiabatic compressibility and show a behavior similar to that of the compressibility and inverse to the ultrasonic velocity.

The graphical representation of intermolecular free length is shown in Figure 2 where the free length decreases with increasing mole fraction of Li₂SO₄. The reason is that increasing the number of larger ions in a given volume leads to decrease in gap between the molecules of two species (solute-solvent). The decreasing free length shows a sudden increase at a specific mole fraction (0.7) of Li₂SO₄ and on further increasing the mole fraction the intermolecular free length again decreases non linearly, there by indicating that there is a significant interaction present between solute and solvent molecules, due to which structural arrangements are considerably affected. A number of other workers also indicated the similar trends about intermolecular free length as indicated in present study [16,17].

Relaxation Time () 

When we pass ultrasonic waves in any liquid some energy is transferred to the molecules of solution as the finite acoustic impedance of liquid restricts the free movement of ultrasonic wave through it. The amount of energy passed to a given volume of liquid grows exponentially with time to its final value and is characterized by a finite time constant which is known as the relaxation time (t). The Shear's relaxation time is a better and more informative parameter than the compressibility (b) as it incorporates Sear's viscosity effect also. 

The values of relaxation time (t) for all possible mole fractions of binary mixture are presented in Table 3 at temperature 303K, 308K, 313K and 318K and the variation of relaxation time with increasing mole fraction of Li₂SO₄ is shown graphically in Figure 3 On increasing mole fraction of Li₂SO₄ the relaxation time increases non linearly and at a specific mole fraction (0.7) it shows a sudden decrease and on further increasing the mole fraction, the relaxation time again starts increasing. This specific mole fraction is exactly same as that observed in case of velocity, adiabatic compressibility, acoustic impedance and intermolecular free length which confirm the complex formation and strong ion solvent interactions in binary mixture at 0.7 mole fraction of Li₂SO₄. Dange [13] has reported the increase in relaxation time with increasing mole fraction in binary mixtures of Nicotinic acid in methanol solutions at 288, 298 and 308 K and indicated the presence of molecular interactions by addition of solute concentration at given temperature. He also reported decrease in relaxation time with increase in temperature at all mole fractions. Similar results are shown in Figure 3 in our present study. 

Molar Volume

For the binary mixture the values of molar volume (V_m) are presented in Table 4 for all mole fractions at temperature 303K, 308K, 313 and 318K. Since in a binary mixture two components are mixed in varying proportions thus to calculate the molar volume, we have first calculated the effective mass (M_eff) of all combination of binary mixture. Then dividing the effective mass of binary mixture of any specific mole fraction by its density (determined experimentally) we have calculated the molar volume of binary mixture for every mole fraction under consideration.

Graphical representation of molar volume is show in Figure 4 where molar volume increases non linearly with increasing mole fraction and with increasing temperature the molar volume gets increased for every mole fraction. As for any specific mole fraction M_eff remains the same at all temperature and density decreases with increasing temperature thus molar volume gets increased with increase in temperature.

Figure 3: Variation of Relaxation Time (×10^-10sec.) for the Binary Mixture of LiCl and Li₂SO₄ with Varying Mole Fraction

Figure 4: Variation of Molar Volume (m³/mole) for the Binary Mixture of LiCl and Li₂SO₄ with Varying Mole Fraction

Figure 5: Variation of Molar Sound Velocity for the Binary Mixture of LiCl and Li₂SO₄ with Varying Mole Fraction

Molar Sound Velocity

Using the values of molar volume, we have calculated the values of an important parameter called molar sound velocity or Rao's molar sound function (R). The values of molar sound velocity are presented in Table 5 and their graphical representation is shown in Figure 5 for binary mixture at temperature 303K, 308K, 313K and 318K. On increasing the mole fraction of Li₂SO₄ molar sound velocity increases non linearly at all temperatures which again supports the existence of ion solvent interactions and complex formation. Similar nonlinear behavior of molar sound velocity is reported earlier by Thorat [18]. The molar sound velocity depends directly on cube root of ultrasonic velocity thus it shows the behavior quite similar to that shown by ultrasonic velocity. The molar sound velocity also increases on increasing the temperature for all mole fractions.

From the above discussion it is quite clear that the variation of acoustic and thermodynamic parameters with concentration and temperature strongly supports the existence of molecular interactions in the binary mixture. Further the sudden rise or fall in various parameter at the same specific mole fraction (0.7) of Li₂SO₄ confirm the complex formation at this mole fraction. 

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